Mathematical and computer simulation for the appearance of dimple defect by cold combined extrusion

Abstract

The article is considered a comparative analysis for predicting defect such as dimple by energy method of power balance, upper bound method and finite element method. The upper bound method takes into account the geometrical position and dimension of the dimple, the criterion for the formation in dimple by energy method of power balance is the presence of a minimum point in the function of relative pressure on the relative velocity of metal outflow in the vertical direction. New engineering calculations for the relative pressure are developed in combined radialbackward extrusion process by using a kinematic module with fillet. A comparative analysis of the obtained data has been carried out by energy method of power balance, upper bound method, computer simulation by Qform 2/3D program and experimental data. Rationality of using the energy method of power balance in view of its efficiency and the possibility of taking into account various friction conditions and the presence of fillet on the matrix, as well as smaller deviations from the results of finite element simulation and experimental data have been defined. Providing more conditions that are favorable for friction in the bottom of the billet and in the flange area in comparison with the friction conditions on the glass wall contribute to delay in the dimple appearance. It was found that the radius of fillet makes it possible to delay the dimple appearance by the approximately (0,4 ÷ 0.5R) mm for the entered radius of fillet R. This allows us to expand the possibilities of obtaining parts with a flange by combined radial-backward extrusion without the formation of a defect such as dimple.